Browsing Department of Mathematics by Title

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We study the representation theory of the solution space of the one-dimensional Schrödinger equation with time-dependent potentials that possess sl₂-symmetry. We give explicit local intertwining maps to multiplier ...

Topological inverse limits play an important in the theory of dynamical systems and in continuum theory. In this dissertation, we investigate classical inverse limits of Julia sets and set-valued inverse limits of arbitrary ...

Littlejohn and Wellman developed a general abstract left-definite theory for a
self-adjoint operator A that is bounded below in a Hilbert space (H,(‧,‧)). More
specifically, they construct a continuum of Hilbert spaces ...

For a ﬁeld F and the polynomial ring F [x] in a single indeterminate, we deﬁne
Ḟ [x] = {α ∈ End_F(F [x]) : α(ƒ) ∈ ƒF [x] for all ƒ ∈ F [x]}. Then Ḟ [x] is naturally isomorphic to F [x] if and only if F is inﬁnite. If F ...

In this dissertation we answer the following question: If X is a Cantor set and T: X → to X is a homeomorphism, what possible orbit structures can T have? The answer is given in terms of the orbit spectrum of T. If X is a ...

In this work, a special class of time-varying linear systems in the arbitrary time scale setting is examined by considering the qualitative properties of their solutions. Building on the work of J. DaCunha and A. Ramos, ...

We are interested in computing eigenvalues and eigenvectors of large matrices and in solving large systems of linear equations. Restarted versions of both the symmetric and nonsymmetric Lanczos algorithms are given. For ...

In this work we explore various piston configurations with different types of potentials. We analyze Laplace-type operators P=-g^ij ∇^E_i ∇ ^E_j+V where V is the potential. First we study delta potentials and rectangular ...

In this dissertation, we are concerned with uniqueness and existence of solutions of certain types of boundary value problems for fourth order differential equations. In particular, we deal with uniqueness implies uniqueness ...

For the third order ordinary differential equation,
$y'''=f(x,y,y',y'')$, it is assumed that, for some $m\geq 4$,
solutions of nonlocal boundary value problems satisfying
\[y(x_1)=y_1,\ y(x_2)=y_2,\] \[y(x_m)-\sum_{i= ...